Numerical verification of vibration-based damage detection algorithm for wind turbine tower

Cong-Uy Nguyen1), Thanh-Canh Huynh2), Jae-Hyung Park2)

and Jeong-Tae Kim3)

1),2),3)Department of Ocean Engineering, Pukyong National University, 45 Yongso-ro, Nam-gu, Busan, Korea

3) idis@pknu.ac.kr

ABSTRACT

In this study, the feasibility of vibration-based structural damage detection for wind turbine tower structures subjected to a harmonic force excitation is numerically evaluated. Firstly,

the algorithm of vibration-based damage detection for the wind turbine tower (WTT) is visited. The natural frequency change, modal assurance criterion (MAC) and frequency-

response-ratio assurance criterion (FRRAC) are utilized to recognize changes in dynamic characteristics due to a structural damage. Secondly, a finite element model based on a real wind turbine tower is established in a structural analysis program, Midas FEA. The

harmonic force is applied at the rotor level as a presence of excitation. Several structural damage scenarios are numerically simulated in segmental joints of the wind turbine model.

Finally, the natural frequency change, MAC and FRRAC algorithms are employed to identify the structural damage occurred in the finite element model. The results show that

these criteria could be used as promising damage existence indicators for the damage alarming in wind turbine supporting structures.

1. INTRODUCTION

Renewable wind energy has been receiving a significant attention of many governments. This is a promising sector because the wind energy produces no greenhouse gas, which is a main cause of global warming. In Europe, with a total installed capacity of 153.7 GW, the wind energy now overtakes coal as the second largest form of power generation capacity in 2016. It is reported that, electricity generation from wind energy covers 10.4 % of the EU-28 total electricity demand (Pineda et al, 2016). In order

1 Graduate Student 2 Post-doctoral Fellow 3 Professor

to fulfill clean energy demand, more wind turbine towers will be installed in the coming years. The strong investment into the wind energy harvest leads to consideration of safety and durability of wind turbine tower. During their lifetime, the slender vertical wind tower exposes to strong winds frequently that can lead to large vibration and repeated stress cycles causing damage in structure (Benedetti et al. 2011). Therefore, the wind turbine towers are monitored and maintained to ensure the safety as well as integrity of system.

It is well-known that the structural damage causes a change of mechanical parameters such as mass, stiffness and damping. Consequently, it alters the dynamic response of the system such as acceleration and modal parameters (Pandey et al. 1994). In the past, there were considerable efforts in vibration-based structural health monitoring which utilized dynamic measurement to extract damage-sensitive features. Many researchers employed the change in natural frequencies to detect structural damages (Vandiver. 1977, Farrar et al. 1994). Some researches consider mode shape changes as an indication of damages in structure (Kim et al. 1995, Kim et al. 2003). There were other studies on mode shape curvature, flexibility, stiffness matrix (Doebling et al. 1998). However, there have been only a few studies conducted on the wind turbine tower using vibration-based structural health monitoring. Nguyen et al. (2015) attempted to detect damage in a numerical model of a wind turbine structure by using the frequency-based and mode shape-based damage detection methods. Nguyen et al. (2017) employed a hybrid impedance and vibration-based algorithms for the damage detection in a lab-scaled wind turbine model. Despite of their attempts, there exists a need to simulate a dynamic behavior of the real-scaled wind turbine structures under a real operation condition such as wind force excitation. There is also a need to comparatively examine the sensitivity of damage indicators for an establishment of the real-time health monitoring system of wind turbines in practices.

This study has been motivated to numerically verify the vibration-based structural damage detection algorithm for wind turbine structures subjected to harmonic force excitation. Firstly, the theory of vibration-based damage detection for the WTT is visited. The natural frequency change, MAC and FRRAC are utilized to recognize changes in dynamic characteristics due to the structural damage. Secondly, the finite element model based on a real wind turbine tower is established in a structural analysis program, Midas FEA. The harmonic force is applied at the rotor level as the presence of excitation. Several structural damage scenarios are numerically simulated in segmental joints of the wind turbine model. Finally, the natural frequency change, MAC and FRRAC indices are employed to identify the structural damage occurred in the finite element model. The results show that these indices could be used as promising damage indicators for the damage alarming in the WTT.

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2.2. Modal Parameters Identification Method Provided that the structure has NE elements and N nodes. By assuming that the

structure behaves linearly, the acceleration response vector at a certain time t for a multi-degree of freedom can be written as

(1)

in which M , C and K are mass, damping and stiffness matrix of the system. , ,

are the displacement, velocity and acceleration response vectors. As described in Eq. (1), the acceleration responses at any location ( , … contains the information of structure ( M , C and K . From these vibration responses, the modal analysis can be performed in time-domain or frequency-domain to extract modal parameters. As the frequency-domain method, frequency domain decomposition (FDD) method is fast and accurate compared to other methods. Therefore, it is broadly used for experimental modal analysis. The FDD method utilizes the singular value decomposition of the power spectral density (PSD) matrix (Brinker et al. 2000, Yi and Yun 2004). The

PSD matrix )(yyS can be constructed by cross-spectrums for all measured accelerations

as

ω ω (2) where n is the number of sensors. Then the PSD matrix is decomposed by using singular value decomposition (SVD) algorithm as

∑ (3)

where )(Σ is a diagonal matrix containing the singular values )(i ),...,1( ni of its PSD

matrix, )(U and )(V are unitary matrices. )(U is equal to )(V since )(yyS is

symmetric. When peak frequencies in the first singular values )(1 are found, the mode

shapes are extracted from anyone of column vectors of )( mU at the corresponding peak

frequencies. The natural frequencies and mode shapes, which are extracted from the FDD method, are prepared for the damage detection criterions as in following section.

2.3. Damage Alarming Criteria Natural frequency change The equation of natural frequency change is written as

- (4)

in which the , are the natural frequency of undamaged baseline and damaged structure. Because the structural stiffness is reduced due to the damage existence, the natural frequency change is negative consequently. Modal assurance criterion In vibration-based method, the modal assurance criterion (MAC) is popular for quantitative comparison of modal vectors. It determines the level of linear correlation between two sets of modes measure before and after the occurrence of damage (West 1984). The variation of mode shape vector between each damage scenario and intact one is examined by modal assurance criterion as

, ∗∗

∗ ∗ (5)

where , ∗are the Eigen vectors in mode i of intact and damage scenarios respectively. If the structure stays intact, the modal assurance criterion will be unity. While it is lower than unity according to damage existence. Frequency-response-ratio assurance criterion As shown in Eq. (1), with the known force vector , change in acceleration signals can represent of damage occurrence. However, the external excitation is usually not determined in field practices. Therefore, the frequency-response-ratio assurance criterion (FRRAC) is selected as a damage indicator because it can eliminate the effect of external force. The FRRAC is computed simply by using two acceleration data measured from two different sensors (Kim et al. 2010). The frequency response ratio between signals from location i and i+1 is defined as

,S , ωS , ω

(6)

where , and , are cross-spectral and auto-spectral density functions in Eq. (6) respectively. By comparing a frequency-response-ratio measured at an undamaged baseline state to the corresponding one at subsequent damaged state, the FRRAC is defined, as follows

, .

. . (7)

where the subscripts u and d denote the undamaged baseline state and its corresponding damaged state in Eq. (7). This equation represents the linear relationship between the undamaged frequency-response-ratio FRRu and damage frequency-response ratio FRRd. The FRRAC is always unity if the structure is intact. Otherwise, it gets lower than unity with respect to damage occurrence. The relative change of FRRAC is computed from Eq. (8) and the , is always unity while the , is under unity with damage occurrences.

, ,

,x100% (8)

3. FINITE ELEMENT ANALYSIS OF WTT

3.1. Description of Finite Element Model The finite element model is based on a real wind turbine tower, which is located in

Hankyung II Wind Park, Jeju Island, Korea. The type of wind turbine tower is V90-3.0 MW with nominal rating 3000 kW. The cut-in wind speed is 4 m/s while the cut-out and 25 m/s. There are 3 blades up wind direction. Nacelle and Rotor weighs 68 and 39.8 ton respectively. The real structure is 80 m high including hub. There are 4 main segments in the tower. Each main segment has a flange at 2 tips so each one combines together through bolt connections. The first segment is embedded in foundation and only 0.55m is above the foundation surface. The second segment is 19.21m long while the two remaining segments are around 29 m. Each main segment is formed by several sections with thickness changing along elevation. The Table 1 lists the variation of section’s thickness with respect to the increasing height. The tubular tower material is S355 J2G31 with 2 % damping ratio. The top level diameter is 2.316 m and the bottom level is 4.150 m. The finite model is established by a commercial structural program, MIDAS FEM as in Fig. 2. The tower is modeled by shell elements with thickness varying from 40 mm to 16 mm as real design. At any section, there are always 36 divisions along perimeter. The height of shell element is five times its width. On the top of model, the rotor and nacelle are simulated as independent lump mases. These masses are linked rigidly to the top flange of wind turbine structure. Wind turbine model is fixed at the bottom as a boundary condition. The modal analysis of intact structure reveals the first 4 mode shapes along the X direction as in Fig. 4. The rotor and nacelle axis is always perpendicular with the tower in every modes due to rigid link model.

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3.2. Simulation of Harmonic Forced Excitation The model is excited by a harmonic force at the rotor location. The excitation acts

along the wind direction, which is the X direction in FEM model. The function of force is F = 10sin 40 ) (kN).

Table 2. Sensor location on WTT model Sensor ID Location Elevation (m)

S1 Flange 1 0.55 S2 - 10.50 S3 Flange 2 19.76 S4 - 30.17 S5 - 40.58 S6 Flange 3 48.77 S7 - 58.62 S8 - 68.46 S9 Flange 4 77.85

S10 Hub 78.93 It is assumed that there is an array of sensors including 10 accelerometers equipped

along the interior of tower as Fig. 3. The signal from flanges are recorded by sensor S1, S3, S6 and S9. The vibrational response of hub is also tracked using sensor S10. Every acceleration signal is extracted from time history analysis by Midas FEM. Afterwards, modal parameters are extracted by the FDD method.

3.3. Structural Damage Scenarios

Four structural damage scenarios were investigated as shown in Table 3. The damage locations are assumed in connections between consecutive segments of tower. These segmental joints are vulnerable during operation under wind load. The damage is simulated as the percentage of reduction in the elastic modulus. In case 1, the first flange is simulated with 25 % reduction in the stiffness. The same assumption is in case 4 with only single damage location. Multi-damage investigation is in case 2 and 3 where severe damage occurs simultaneously at two random flanges. 20 % is the percentage of damage severity of two simultaneous flanges which are examined in this analysis.

Table 3. Structural damage scenarios of WTT model

Damage case

Damage simulation Location Elevation (m) Severity

Intact - - - 1 Flange 1 0.55 25% 2 Flange 1 and 3 0.55 and 48.765 20% and 20% 3 Flange 2 and 4 19.76 and 77.85 20% and 20% 4 Flange 4 77.85 25%

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In the power spectral density, peaks indicate vibration modes of wind turbine tower under excitation as in Fig. 6. It is clear that there are four peaks which indicate first four modes along X direction respectively. The noise in plot is caused by the aliasing phenomenon. As shown in Fig. 7, the extracted modal parameters of intact model including the mode shape and natural frequency are similar to the modal analysis. Due to the damage existence, the peaks in PSD shift to the left with respect to the intact one. The shifts get larger for higher modes compared to lower ones as in Fig. 8.

4.2. Structural Damage Alarming by Natural Frequency Change

The modal frequencies of all scenarios are illustrated in Table 4. It is clear that modal frequency decreases when damage occurs in WTT. The first natural frequency does not change in every case. Fig. 9 shows that the natural frequency reduction increases with respect to higher mode.

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1 0.3113 0.3113 0.3113 0.3113 0.3113 2 2.2583 2.2522 2.2522 2.2552 2.2568 3 5.4092 5.4016 5.4016 5.3909 5.4001 4 9.7931 9.6893 9.6878 9.6939 9.6954

Fig. 9 Relative reduction in natural frequencies due to damage 4.3. Structural Damage Alarming by MAC

The mode shapes are revealed from the FDD method. As in Fig. 10, the 1st and 2nd mode shapes are nearly the same in every case while the 3rd and 4th ones change along each scenario. The vertical line stands for the center of static structure. The MAC is computed between intact scenario and each damage one by Eq. (5). The MAC is nearly 1 for mode 1 and 2 because there is little change of the 1st and 2nd modes in every case. However, this index decreases larger in mode 3 and 4 as presented in Fig. 11.

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Fig. 11 MAC change due to structural damage

4.4. Structural Damage Alarming by FRRAC The acceleration signals from all sensors are utilized to calculate the ASD and CSD

from 0 Hz to 25 Hz, which is the Nyquist frequency. Afterwards, the FRR is computed as Eq. (6). Within sensor S3 and S6, the FRR of intact case and damaged cases are presented as in Fig. 12. From all of sensors, the FRRAC is by Eq. (7). Fig. 13 shows the relative change of the FRRAC between the intact and every damaged case by Eq. (8). The FRRAC succeeds in recognition of damage occurrences in every case. It is noted that the FRRAC from sensor 3 to 7, which is near the damage locations, is more sensitive than the remaining.

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Innovation Program funded by Ministry of Land, Infrastructure and Transport (MOLIT). The graduate student involved in this research was also supported by the Brain Korea 21 Plus program of Korean Government.

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